Efficient generic calibration method for general cameras with single centre of projection

Generic camera calibration is a non-parametric calibration technique that is applicable to any type of vision sensor. However, the standard generic calibration method was developed with the goal of generality and it is therefore sub-optimal for the common case of cameras with a single centre of projection (e.g. pinhole, fisheye, hyperboloidal catadioptric). This paper proposes novel improvements to the standard generic calibration method for central cameras that reduce its complexity, and improve its accuracy and robustness. Improvements are achieved by taking advantage of the geometric constraints resulting from a single centre of projection. Input data for the algorithm is acquired using active grids, the performance of which is characterised. A new linear estimation stage to the generic algorithm is proposed incorporating classical pinhole calibration techniques, and it is shown to be significantly more accurate than the linear estimation stage of the standard method. A linear method for pose estimation is also proposed and evaluated against the existing polynomial method. Distortion correction and motion reconstruction experiments are conducted with real data for a hyperboloidal catadioptric sensor for both the standard and proposed methods. Results show the accuracy and robustness of the proposed method to be superior to those of the standard method

Self-similar prior and wavelet bases for hidden incompressible turbulent motion

This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompressible isotropic turbulence. Nevertheless, the associated maximum a posteriori involves a fractional Laplacian operator which is delicate to implement in practice. To deal with this issue, we propose to decompose the divergent-free fBm on well-chosen wavelet bases. As a first alternative, we propose to design wavelets as whitening filters. We show that these filters are fractional Laplacian wavelets composed with the Leray projector. As a second alternative, we use a divergence-free wavelet basis, which takes implicitly into account the incompressibility constraint arising from physics. Although the latter decomposition involves correlated wavelet coefficients, we are able to handle this dependence in practice. Based on these two wavelet decompositions, we finally provide effective and efficient algorithms to approach the maximum a posteriori. An intensive numerical evaluation proves the relevance of the proposed wavelet-based self-similar priors.Comment: SIAM Journal on Imaging Sciences, 201

Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration

Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach